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Shall we take Solow seriously??

Shall we take Solow seriously??. Empirics of growth Ania Nici ń ska Agnieszka Post ę pska Pawe ł Zaboklicki. Solow Assuming neoclassical production function steady state level of capital per capita is determined by saving and population growth rates. Mankiw, Romer &Weil

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Shall we take Solow seriously??

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  1. Shall we take Solow seriously?? Empirics of growth Ania Nicińska Agnieszka Postępska Paweł Zaboklicki

  2. Solow Assuming neoclassical production function steady state level of capital per capita is determined by saving and population growth rates Mankiw, Romer &Weil Yes – predicted directions of influence are consistent with the data… but…we need to add accumulation of human capital to get the right magnitudes Original & augmented models:

  3. Why? • For any given rate of human capital accumulation higher saving or lower population growth leads to a higher level of income and thus a higher level of human capital. • Omitting human capital accumulation causes bias if correlated with saving and population growth rates.

  4. Including a proxy for human capital as an additional explanatory variable in the regression equation leads to magnitudes predicted by Solow. The augmented model accounts for about 80% of the cross country variation in income!!!! We will prove that…

  5. So…after all Solow was right – he just forgot about some details… happens!!!!

  6. What about convergence??

  7. We will prove that once accounting for the saving and population growth rate we observe convergence at roughly the rate that Solow predicted.

  8. Data • We used data from Barro and Lee data set. It contains different country set to the one used by authors so our results vary in magnitudes. However, the spirit remains unchanged!

  9. Data cont. We have data from years 1960-1985 for 121 countries divided into three groups: • 1 – non-oil countries • 2 – intermediate countries • 3 – OECD countries The dataset includes real income, investments, population growth and proxy for human capital accumulation.

  10. Basic model • First, we will look at the results obtained from the basic model equation estimation, which takes the following form:

  11. We want to investigate whether real income is higher in countries with higher saving rate and lower in countries with higher values of n+g+d.

  12. We assume that g+d =0.05 is constant across countries, where g reflects the advancement of knowledge, which is not country specific.

  13. Results (OLS): • gen lny=ln(gdp) • gen lns=ln(inv) • gen lnngd=ln(gpop +0.05) • reg lny lns lnngd if group1==1 • Source | SS df MS Number of obs = 566 • -------------+------------------------------ F( 2, 563) = 333.72 • Model | 324.412641 2 162.20632 Prob > F = 0.0000 • Residual | 273.650411 563 .486057568 R-squared = 0.5424 • -------------+------------------------------ Adj R-squared = 0.5408 • Total | 598.063052 565 1.05851868 Root MSE = .69718 • ------------------------------------------------------------------------------ • lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] • -------------+---------------------------------------------------------------- • lns | .7575753 .0404936 18.71 0.000 .6780384 .8371122 • lnngd | -2.186215 .1768619 -12.36 0.000 -2.533605 -1.838825 • _cons | 3.342269 .4937159 6.77 0.000 2.372519 4.312019 • ------------------------------------------------------------------------------

  14. Results (panel): tis czas iis kraj xtreg lny lns lnngd if group1==1 • Random-effects GLS regression Number of obs = 566 • Group variable (i): kraj Number of groups = 97 • R-sq: within = 0.0849 Obs per group: min = 2 • between = 0.6024 avg = 5.8 • overall = 0.5421 max = 6 • Random effects u_i ~ Gaussian Wald chi2(2) = 111.65 • corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 • ------------------------------------------------------------------------------ • lny | Coef. Std. Err. z P>|z| [95% Conf. Interval] • -------------+---------------------------------------------------------------- • lns | .3205264 .0401647 7.98 0.000 .2418049 .3992478 • lnngd | -.9881011 .1455752 -6.79 0.000 -1.273423 -.7027789 • _cons | 5.629819 .3984202 14.13 0.000 4.84893 6.410708 • -------------+---------------------------------------------------------------- • sigma_u | .62736692 • sigma_e | .2624178 • rho | .85109147 (fraction of variance due to u_i)

  15. Human capital the fraction of the eligible population (aged 12-17) enrolled in secondary school multiplied by the fraction of population at working-age that is of school age (15-17) for country j and time period i. assumed to be constant over time and equal to 0.05 for all countries

  16. Introducing human capital xtreg lny lns lnngd lnSCHOOL if group1==1 4.17918 5.703551 -------------+---------------------------------------------------------------- sigma_u | .48950053 sigma_e | .23470675 rho | .81307219 (fraction of variance due Random-effects GLS regression Number of obs = 497 Group variable (i): kraj Number of groups = 86 R-sq: within = 0.3090 Obs per group: min = 1 between = 0.7432 avg = 5.8 overall = 0.7029 max = 6 Random effects u_i ~ Gaussian Wald chi2(3) = 363.77 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ lny | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- lns | .3002022 .0389558 7.71 0.000 .2238503 .3765542 lnngd | -1.038666 .1443974 -7.19 0.000 -1.32168 -.7556523 lnSCHOOL | .2845598 .021147 13.46 0.000 .2431125 .3260071 _cons | 4.941366 .3888772 12.71 0.000 to u_i) ------------------------------------------------------------------------------ .

  17. Hausman test Hausman specification test ---- Coefficients ---- | Fixed Random lny | Effects Effects Difference -------------+----------------------------------------- lns | .2198654 .3002022 -.0803368 lnngd | -.8024757 -1.038666 .2361903 lnSCHOOL | .2400482 .2845598 -.0445116 Test: Ho: difference in coefficients not systematic chi2( 3) = (b-B)'[S^(-1)](b-B), S = (S_fe - S_re) = 165.07 Prob>chi2 = 0.0000 We reject Ho hypothesis and run fixed effect regression

  18. Fixed effect regression xtreg lny lns lnngd lnSCHOOL if group1==1, fe Fixed-effects (within) regression Number of obs = 497 Group variable (i): kraj Number of groups = 86 R-sq: within = 0.3099 Obs per group: min = 1 between = 0.7441 avg = 5.8 overall = 0.7026 max = 6 F(3,408) = 61.07 corr(u_i, Xb) = 0.5936 Prob > F = 0.0000 ------------------------------------------------------------------------------ lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- lns | .2198654 .0420508 5.23 0.000 .1372021 .3025288 lnngd | -.8024757 .1530299 -5.24 0.000 -1.103301 -.5016503 lnSCHOOL | .2400482 .0222506 10.79 0.000 .1963082 .2837883 _cons | 5.511256 .4062469 13.57 0.000 4.712658 6.309854 -------------+---------------------------------------------------------------- sigma_u | .6270438 sigma_e | .23470675 rho | .87711176 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(85, 408) = 27.03 Prob > F = 0.0000

  19. gen rhs1= lnngd-lns gen rhs2= lnSCHOOL-lns

  20. Restricted fixed effect regression xtreg lny rhs1 rhs2 if group1==1, fe Fixed-effects (within) regression Number of obs = 497 Group variable (i): kraj Number of groups = 86 R-sq: within = 0.3023 Obs per group: min = 1 between = 0.7273 avg = 5.8 overall = 0.6850 max = 6 F(2,409) = 88.61 corr(u_i, Xb) = 0.5756 Prob > F = 0.0000 ------------------------------------------------------------------------------ lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- rhs1 | -.4935334 .0456002 -10.82 0.000 -.5831734 -.4038934 rhs2 | .2524585 .021553 11.71 0.000 .2100899 .294827 _cons | 6.339631 .1076709 58.88 0.000 6.127974 6.551289 -------------+---------------------------------------------------------------- sigma_u | .63733151 sigma_e | .23570005 rho | .87968598 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(85, 409) = 28.91 Prob > F = 0.0000

  21. Convergence . reg lny lnY60 if group1==1 Source | SS df MS Number of obs = 546 -------------+------------------------------ F( 1, 544) = 522.06 Model | 294.766441 1 294.766441 Prob > F = 0.0000 Residual | 307.152329 544 .564618253 R-squared = 0.4897 -------------+------------------------------ Adj R-squared = 0.4888 Total | 601.918771 545 1.10443811 Root MSE = .75141 ------------------------------------------------------------------------------ lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- lnY60 | .0003215 .0000141 22.85 0.000 .0002938 .0003491 _cons | 6.902612 .0449259 153.64 0.000 6.814363 6.990862 ------------------------------------------------------------------------------

  22. . xtreg lny lnY60 lns lnngd if group1==1 Random-effects GLS regression Number of obs = 540 Group variable (i): kraj Number of groups = 91 R-sq: within = 0.0562 Obs per group: min = 5 between = 0.6457 avg = 5.9 overall = 0.6097 max = 6 Random effects u_i ~ Gaussian Wald chi2(3) = 206.77 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ lny | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- lnY60 | .0002534 .0000278 9.10 0.000 .0001988 .0003079 lns | .2594275 .0403126 6.44 0.000 .1804161 .3384388 lnngd | -.7506613 .1733739 -4.33 0.000 -1.090468 -.4108547 _cons | 5.574069 .4559533 12.23 0.000 4.680417 6.467721 -------------+---------------------------------------------------------------- sigma_u | .54971182 sigma_e | .26339936 rho | .81327701 (fraction of variance due to u_i) ------------------------------------------------------------------------------ Controlling for saving and population growth

  23. Hausman test • . xthausman • Hausman specification test • ---- Coefficients ---- • | Fixed Random • lny | Effects Effects Difference • -------------+----------------------------------------- • lns | .1734279 .2594275 -.0859996 • lnngd | -.6418418 -.7506613 .1088195 • Test: Ho: difference in coefficients not systematic • chi2( 2) = (b-B)'[S^(-1)](b-B), S = (S_fe - S_re) • = 31.07 • Prob>chi2 = 0.0000

  24. Controlling for saving and population growth • . xtreg lny lnY60 lns lnngd if group1==1, fe • Fixed-effects (within) regression Number of obs = 540 • Group variable (i): kraj Number of groups = 91 • R-sq: within = 0.0571 Obs per group: min = 5 • between = 0.6378 avg = 5.9 • overall = 0.5657 max = 6 • F(2,447) = 13.54 • corr(u_i, Xb) = 0.6823 Prob > F = 0.0000 • ------------------------------------------------------------------------------ • lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] • -------------+---------------------------------------------------------------- • lnY60 | (dropped) • lns | .1734279 .0432074 4.01 0.000 .088513 .2583427 • lnngd | -.6418418 .1774066 -3.62 0.000 -.9904963 -.2931873 • _cons | 6.26194 .471011 13.29 0.000 5.336269 7.18761 • -------------+---------------------------------------------------------------- • sigma_u | .88996904 • sigma_e | .26339936 • rho | .91945985 (fraction of variance due to u_i) • ------------------------------------------------------------------------------ • F test that all u_i=0: F(90, 447) = 27.41 Prob > F = 0.0000

  25. Controlling for saving and population growth • . reg lny lnY60 lns lnngd if group1==1 • Source | SS df MS Number of obs = 540 • -------------+------------------------------ F( 3, 536) = 342.36 • Model | 387.410632 3 129.136877 Prob > F = 0.0000 • Residual | 202.178054 536 .377197862 R-squared = 0.6571 • -------------+------------------------------ Adj R-squared = 0.6552 • Total | 589.588686 539 1.09385656 Root MSE = .61416 • ------------------------------------------------------------------------------ • lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] • -------------+---------------------------------------------------------------- • lnY60 | .0001856 .0000155 11.95 0.000 .0001551 .0002161 • lns | .6007277 .0406437 14.78 0.000 .5208872 .6805683 • lnngd | -1.204025 .2259398 -5.33 0.000 -1.647861 -.7601891 • _cons | 5.195703 .5954142 8.73 0.000 4.026072 6.365335 • ------------------------------------------------------------------------------

  26. Controlling for human capital • . reg lny lnY60 lns lnngd lnSCHOOL if group1==1 • Source | SS df MS Number of obs = 471 • -------------+------------------------------ F( 4, 466) = 373.07 • Model | 376.353388 4 94.088347 Prob > F = 0.0000 • Residual | 117.526225 466 .252202199 R-squared = 0.7620 • -------------+------------------------------ Adj R-squared = 0.7600 • Total | 493.879613 470 1.05080769 Root MSE = .5022 • ------------------------------------------------------------------------------ • lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] • -------------+---------------------------------------------------------------- • lnY60 | .0001264 .0000134 9.46 0.000 .0001002 .0001527 • lns | .3148332 .0456057 6.90 0.000 .2252149 .4044514 • lnngd | -1.093758 .2040205 -5.36 0.000 -1.494672 -.6928435 • lnSCHOOL | .3618771 .0245546 14.74 0.000 .3136256 .4101285 • _cons | 4.347212 .5360951 8.11 0.000 3.293749 5.400675 • ------------------------------------------------------------------------------

  27. Restricted regression • . reg lny lnY60 rhs1 rhs2 if group1==1 • Source | SS df MS Number of obs = 471 • -------------+------------------------------ F( 3, 467) = 493.21 • Model | 375.396246 3 125.132082 Prob > F = 0.0000 • Residual | 118.483367 467 .253711707 R-squared = 0.7601 • -------------+------------------------------ Adj R-squared = 0.7586 • Total | 493.879613 470 1.05080769 Root MSE = .5037 • ------------------------------------------------------------------------------ • lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] • -------------+---------------------------------------------------------------- • lnY60 | .0001386 .0000118 11.72 0.000 .0001154 .0001619 • rhs1 | -.7030645 .0375851 -18.71 0.000 -.7769213 -.6292077 • rhs2 | .36919 .0243385 15.17 0.000 .3213636 .4170165 • _cons | 5.374257 .0975428 55.10 0.000 5.18258 5.565934 • ------------------------------------------------------------------------------

  28. Conclusions: • We proved that augmented Solow model describes growth well, both in directions of influence and magnitudes. • We also showed that convergence do happen in reality once we compare similar countries in terms of population growth and saving rates.

  29. Cook book procedure for a research project: • Begin as soon as possible: data sets are ‘like a box of chocolates – you never know what you’re gonna get’ • Be patient: ‘read me’ files can be tricky • Attend STATA classes and learn programming or become a ‘copy/paste’ master • Make friends – there is a huge difference between knowing how to do something & doing it.

  30. So…& so it is – just like Solow said it should be… GOOD LUCK!!!!!!

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